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From: martin@entropy.UUCP (Don Martin)
Newsgroups: sci.math
Subject: Re: Need formula for Normal Distribution Simulation
Message-ID: <401@entropy.UUCP>
Date: Thu, 30-Oct-86 01:33:53 EST
Article-I.D.: entropy.401
Posted: Thu Oct 30 01:33:53 1986
Date-Received: Sat, 1-Nov-86 04:49:54 EST
References: <146@helm.UUCP> <5270001@hpfcpf.HP.COM>
Organization: UW MathStat, Seattle
Lines: 29
Summary: Box Mueller Normal deviate problem

In article <5270001@hpfcpf.HP.COM>, rms@hpfcpf.HP.COM writes:
> The following is called the Box-Muller algorithm, and does a very
> good job of generating normal random deviates:
> 
>    1. Generate two uniform random numbers, U1 and U2.
> 
etc.

You need to be careful with the Box-Muller if you use
either a linear congruential or a multiplicative
congruential random number generator for U1 and U2.
Since these are the usual generators included in most
systems the problem is common. What happens is that
the sequential dependency in U1 and U2 cuase spikes
in the tail of the distribution. This was published
in Applied Statistics about 7 years ago. To fix this
either:

1) see the Applied Stat. article about exchanging orders.
2) put in a shuffle generator.
3) throw away one uniform random between U1 and U2
4) use two seperate uniform generators.
5) use another type of generator such as a shift register.

Also you can just generat X1 and not X2.

Hope this helps avoid a potential problem.

Donald C. Martin